Descriptive
and Inferential Statistics and their Limitations
Descriptive Statistics:
Descriptive statistics are very important because if we simply presented our raw data it would be hard to visualize what the data was showing, especially if there was a lot of it. Descriptive statistics therefore enables us to present the data in a more meaningful way, which allows simpler interpretation of the data. Descriptive statistics are applied to populations, and the properties of populations, like the mean or standard deviation, are called parameters as they represent the whole population (i.e., everybody you are interested in).Any average, for example, is a descriptive statistic. So, batting averages, average daily rainfall, or average daily temperature are good examples of descriptive statistics.
Inferential Statistics:
Inferential statistics are used to make inferences about the larger population based on the sample. Since a sample is a small subset of the larger population (or sampling frame), the inferences are necessarily error prone. That is, we cannot say with 100% confidence that the characteristics of the sample accurately reflect the characteristics of the larger population (or sampling frame) too.
For example when we want to determine if some treatment is better than another, or if there are differences in how two groups perform. A good book definition is using samples to draw inferences about populations.
Difference between Descriptive Statistics and Inferential statistics:
As seen above, descriptive statistics is concerned with telling about certain features of a data set. Although this is helpful in learning things such as the spread and center of the data we are studying, nothing in the area of descriptive statistics can be used to make any sort of generalization. In descriptive statistics measurements such as the mean and standard deviation are stated as exact numbers. Though we may use descriptive statistics all we would like in examining a statistical sample, this branch of statistics does not allow us to say anything about the population.
Inferential statistics is different from descriptive statistics in many ways. Even though there are similar calculations, such as those for the mean and standard deviation, the focus is different for inferential statistics. Inferential statistics does start with a sample and then generalizes to a population. This information about a population is not stated as a number. Instead we express these parameters as a range of potential numbers, along with a degree of confidence.
Descriptive statistics comprises the statistical methods dealing with the collection, tabulation and summarization of data, so as to present meaningful information. Statistical inference, on the other hand, consists of the methods involved with the analysis and interpretation of data that will enable the statistician to develop meaningful inferences about the data. Both subfields are interrelated; while descriptive statistics organizes the collected data in a systematic manner, statistical inference analyzes the data and enables one to produce significant inferences about it.
Limitations:
Descriptive statistics are limited in so much that they only allow you to make summations about the people or objects that you have actually measured.You cannot use the data you have collected to generalize to other people or objects (i.e., using data from a sample to infer the properties/parameters of a population). For example, if you tested a drug to beat cancer and it worked in your patients, you cannot claim that it would work in other cancer patients only relying on descriptive statistics (but inferential statistics would give you this opportunity).
There are two main limitations to the use of inferential statistics. The first and most important limitation, which is present in all inferential statistics, is that you are providing data about a population that you have not fully measured, and therefore, cannot ever be completely sure that the values/statistics you calculate are correct. Inferential statistics are based on the concept of using the values measured in a sample to estimate/infer the values that would be measured in a population; there will always be a degree of uncertainty in doing this. The second limitation is connected with the first limitation. Some, but not all, inferential tests require the user (i.e., you) to make educated guesses (based on theory) to run the inferential tests. Again, there will be some uncertainty in this process, which will have repercussions on the certainty of the results of some inferential statistics
Source:
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http://www2.fiu.edu/~ganapati/4153/regression.html
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